On the insensitivity of the score test for heterogeneity to omitted covariates in multivariate failure time models

The multivariate Weibull distribution often provides a point of departure for modelling repeated, or a sequence of, failure times for a particular individual. It is then natural to want to test the implied assumption of homogeneity, and a number of authors have derived a score test for this purpose; see, for example, Kimber (1996). In the present paper it is shown that the proposed score test for neglected heterogeneity can be insensitive to specification error in the implied log-linear regression structure. Asymptotic local analysis; Heterogeneity; Insensitivity; Multivariate failure time; Omitted variable.